Amid deep party-line divisions, the SenateJudiciary Committee on Thursday approved Congress’ first post-Newtown gun control bill — a proposal to crack down on gun trafficking and straw purchases meant to circumvent the law — but the panel pushed the toughest work off until next week.

With just a single Republican joining them, Democrats powered the trafficking bill through on a 11-7 vote, saying they hoped stiff penalties would make owners think twice before letting their guns fall into the hands of criminals.

But the committee recessed in the middle of debating a bill that would ban military-style semiautomatic rifles and impose caps on the size of ammunition magazines, and lawmakers never even got to legislation that would expand background checks. The panel will return to those thorny issues next week.

Still, Thursday’s vote was the first victory for President Obama and gun control advocates, who have seen their momentum after December’s shooting rampage in a Connecticut elementary school turn into a tough legislative slog.

Mr. Obama and his Democratic allies have insisted that if lawmakers can save just one life with a gun restriction law, they have an obligation to do so.

“The plain, simple blunt fact is that if some, if not all of the beautiful children who perished that day in Newtown, along with the great educators who gave their lives trying to save those children, might well be alive today if [a] ban had been in effect — a ban on military-style assault weapons and the high-capacity magazines,” said Sen. Richard Blumenthal, Connecticut Democrat.

While the federal assault-weapons ban expired in 2004, Connecticut’s similar state law was still in effect on the day of the Newtown massacre. Its definition of “assault weapon,” however, did not cover the killer’s guns, which were legal to own.

Republicans countered that it makes little sense to pass additional legislation without first enforcing existing laws more vigorously.

“I have a hard time explaining to my constituents back home how passing more laws that will go unenforced makes them any safer,” said Sen. John Cornyn, Texas Republican.

Sen. Chuck Grassley of Iowa was the lone Republican to join 10 Democrats in backing the trafficking bill, which makes it illegal to purchase a gun with the intention of transferring it to someone who cannot legally possess one.

“Federal legislation needed on the subjects of straw purchasing and gun trafficking will strengthen efforts to combat illicit firearms,” he said. “When I conducted my oversight of the Justice Department’s failed [Operation] Fast and Furious, I was told by whistleblowers that there were gaps in federal law concerning straw purchasers that should be addressed, and this is our opportunity to do it.”

After finishing the trafficking bill, the committee turned to Sen. Dianne Feinstein’s measure to ban so-called assault weapons and to outlaw high-capacity magazines.

The California Democrat said her legislation has been mischaracterized and even channeled a line from Vice President Joseph R. Biden by rhetorically asking whether anyone would respect a hunter who toted a 30-round magazine and high-powered rifle to go after a deer.

“I’ve been very concerned because the calls have been coming in as if this is some kind of wild-eyed scheme. It is not,” Mrs. Feinstein said.

She said states have enacted similar bans in their own jurisdictions and none of them has been declared unconstitutional by the courts.